A natural question to explore is whether 0-uncloneable security is possible, even for single-bit messages, since 0-uncloneable security means that a cloning adversary \((\mathcal {A},\mathcal {B},\mathcal {C})\)  does not benefit from cloning the ciphertext at all, and hence cannot do better than the trivial strategy of giving the ciphertext to \(\mathcal {B}\)  and having \(\mathcal {C}\)  randomly guess the message. In this section we show that the conjugate encryption of \(\cite {BL19}\)  is not \(0-\) uncloneable secure. To show this, we note that the valid ciphertexts in conjugate encryption for one-bit messages all lie on the \(xz\) -plane of the Bloch Sphere, i.e. they do not have an imaginary phase in the computational basis. Besides, encrypting multi-bit messages is done simply by encrypting each bit separately. The following lemma, which corresponds to the optimal equatorial cloner studied in [1]}, will take advantage of this fact:
